Question

How many grams of potassium chloride must decompose to produce 69.9 milliliters of potassium metal, if the density of potassium is 1.78 g/mL? Show all steps of your calculation as well as the final answer.

KCl → K + Cl2

Answer 1

can u plz explain to me how to solve this i am really confused? @Abhisar

Answer 2

to start, you need the mass percent composition of potassium in KCl.

Can you find that?

Answer 3

50% potassium(1+) 50% chloride(1-)

Answer 4

@Festinger

Answer 5

nope, in terms of mass. 1 mole of K =/= 1 mole of Cl, right?

Answer 6

ok thanks. what do i do after that?

Answer 7

To begin we first have to balance the equation. As a slight detail this process of decomposition of potassium chloride is done by electrical electrolysis.

Answer 8

2K+Cl2=2KCl

Answer 9

So the next step would be to convert the volume of potassium into mass, then into moles.

This is because the balance reaction tells us the molarity between the chemicals; it does not say anything about how it reacts in volume, pressure or mass.

Answer 10

convert the volume of potassium into mass: 100 g
volume of potassium into mass moles: i dont know how to do that

Answer 11

From the periodic table there are values called the molar mass. These will tell you how heavy the element is per mole.

\[\frac{mass}{molar\:mass}=moles\]
Or alternatively.
\[molar\:mass*moles = mass\]
If you notice these 2 forms are the same.

Answer 12

Does the question give the density of potassium as 1.78g/ml?

Answer 13

yes

Answer 14

100 = molar mass X moles how do i ge the molar mass?

Answer 15

I think it should be 124.422g instead of 100g since
\[69.9ml\:\times \:1.78\frac{g}{ml}=124.422g\]

You can find the molar mass from the periodic table.

Answer 16

oh. the molar mass is 74.5513. what do i do then?

Answer 17

I should've used the term atomic weight of potassium instead.

74.5513 is the molar mass of KCl, but currently still working with potassium. We will still need to use this number later though.

With the atomic weight we can find the number of moles of potassium using the equation I typed above:
\[\frac{mass}{atomic\:weight}=amount\:of\:moles\]

Answer 18

amount of mole is: 1.78/74.5513 is this right?

Answer 19

Nope.

\[\frac{1.78\frac{g}{ml}}{74.551\frac{g}{mol}}=0.0239\frac{mol}{ml} \]

Those are not the units of moles. Those are the unit of molar concentration.

Answer 20

We first begin with the balanced reaction of the reaction:
\[2KCl \rightarrow 2K(s) + Cl_{2}(g)\]

We are tasked to find the mass of KCl needed, subject to the condition that we need 69.9ml of potassium metal at the end. To solve this, we have to compare how much potassium we need to have in the balanced equation in moles.

In particular, since we are given that the density of potassium(K) is 1.78g/ml (from the question), we can find the mass of potassium as products. Indeed:
\[69.9ml×1.78\frac{g}{ml}=124.422g\]
You can think that the units cancel out in fractions. Returning to the question, we can now convert the mass of potassium into moles. To do that recall that
\[moles\times atomic\:mass=mass\]
Rearranging yields:
\[\frac{mass}{atomic\:mass}=moles\]
From the periodic table, we find that the mass of potassium to be 39.10. Thus,
\[\frac{124.422g}{39.10\frac{g}{mol}}=3.1821mols\]

Now we are in business! We can now compare how much moles of KCl we need! In particular,
\[\frac{moles\:of\:KCl}{moles\:of\:K}=\frac{2}{2}=1\]
Note that we put the quantity we wish to find on the top. This says that we produce as much K as the KCl decomposed in moles (not mass!). To see this clearly,
\[moles\:of\:KCl=(\frac{moles\:of\:KCl}{moles\:of\:K})*moles\:of\:K\]
I placed the braket on the first term to remind ourselves that this is a ratio, and the second term is the value 3.1821mols we found eariler, and "moles of K" cancels out when you multiply them. Indeed:
\[moles\:of\:KCl=((\frac{2}{2})*3.1821=3.1821mols\]

To convert moles to mass, we recall that:
\[moles*molar\:mass=mass\]
And the molar mass of KCl is
\[atomic\:weight\:of\:Cl + atomic\:weight\:of\:K=39.10+35.45=74.55\frac{g}{mol}\]
Putting it all together,
\[mass\:of\:KCl\:needed=3.1821*74.55=237.2g\]
We need at least 237.2g of KCl to decompose to produce 69.9ml of potassium metal, under the condition that the density of potassium is 1.78g/ml.

Answer 21

thanks you soo much!!!